Particle-laden or droplet-laden turbulent flows occur in many industrial applications and in natural phenomena. Knowledge about the properties of these flows can help to improve the design of unit operations in industry and to predict for instance the occurrence of rain showers. This knowledge can be obtained from experimental research and from numerical simulations. In this paper a review is given of numerical simulation methods for particle-laden flows. There are various simulation methods possible. They range from methods in which all details, including the flow around each particle, are resolved, via point-particle methods, in which for each particle an equation of motion is solved, to Eulerian methods in which equations for particle concentration and velocity are solved. This review puts the emphasis on the intermediate class of methods, the Euler-Lagrange methods in which the continuous phase is described by an Eulerian approach and the dispersed phase in a Lagrangian way with equations of motion for each individual particle.